The price of multi-group transductive learning

2026-06-03

AI Summary

This study investigates the error rate imbalance problem in multi-group transductive learning, revealing that under the transductive setting, the error rates for certain groups can be substantially higher than in the single-group case. Through theoretical analysis, the work establishes—for the first time—that the error penalty in multi-group transductive learning can grow linearly with the number of groups, reaching up to the order of the square root of the sample size, which significantly exceeds the logarithmic bounds known in classical statistical learning theory. The paper derives a tight lower bound on this error penalty, precisely characterizing its fundamental dependence on both the number of groups and the sample size, thereby providing a rigorous theoretical foundation for understanding the trade-off between multi-group fairness and generalization performance.

Abstract

We show every multi-group learner in the transductive setting may incur a multiplicative penalty in its error rate on some group relative to the error rate achievable in the single-group setting, and the penalty can increasing linearly with the number of groups, up to roughly the square-root of the sample size. This stands in stark contrast to optimal multi-group learners in an analogous (group-realizable) statistical setting, where the penalty is always at most logarithmic in the sample size and independent of the number of groups.

Problem

• multi-group learning
• transductive learning
• error rate penalty
• sample complexity
• group fairness

Innovation

• multi-group learning
• transductive learning
• error rate penalty
• sample complexity
• fairness